Esteban Egea-Lopez (11719120), Jose Maria Molina-Garcia-Pardo (11719123), Martine Lienard (11719126) et al. · Figshare · 2021
<p>Magnitude of the total (direct, reflected, diffracted) received electric field at receiver points around a straight perfect conductor edge (square angle between faces, n = 1.5). Receivers are placed on a full circumference of radius s = 20 m around the edge at 1 degree steps. A transmitter at f = 1.8 GHz with vertical polarization is placed at an angle of 45 degrees from the edge closest face and m from the edge. (a) Total received field. (b) Geometry of the scenario.</p>
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L.P. Ivrissimtzis, R. J. Marhefka · Radio Science · 1989
An approximation for the diffraction of an edge wave by the vertex and edges of a conducting trihedron is developed. The edge wave is produced by an electric dipole source located in the vicinity of one of the edges and sufficiently far from the tip of the vertex. The radiation integral of the currents that would be induced over an infinite wedge, which is then truncated, is evaluated asymptotically yielding an endpoint effect. The effect of a fringe current component, excited by the terminating edges, is introduced subsequently. The approximation shows good agreement with method of moments computations and measured data for several flat plate structures.
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Peter V. Polyanskii · SPIE eBooks · 2019
The phenomenon of knife-edge light diffraction was first described in 1665 by Grimaldi, who introduced the term diffraction to define this special kind of light propagation (differing from rectilinear propagation, reflection, and refraction). The concept of diffraction was elaborated on in detail by Newton. It is well known that Newton clearly understood that diffraction is caused by the steplike disrupting homogeneity of the space of the propagation of light, but he could not reconcile this fact with the law of rectilinear light propagation, which is not generally inherent in the wave motion observed in nature (waves at waters’ surfaces, tides, etc.). This was the main discrepancy between Newton’s understanding and Huygens’ explanation of the nature of light. Despite Newton’s discovery of two important optical phenomena (i.e., Newton’s rings and dispersion of light), both of which are now explained by wave theory, Newton hesitated to accept the wave paradigm and was often inclined to use the corpuscular interpretation. It is of interest that some late remarks made by Newton during the singular optics epoch2 give reason to believe that he was on the verge of accepting the wave understanding of light phenomena, at least in terms of the edge diffraction wave (EDW), which is the main topic of consideration here. Nevertheless, this statement seems hyperbolic, as Newton widely discusses the edge effect (rather than on the edge wave) and only uses the term ‘light rays,’ which is attributed to geometrical optics. As such, Newton’s views from those days can only too cautiously be projected to the modern views on the nature of light.
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П. Н. Дагуров, А. В. Дмитриев · 2000
At prediction of radiowave attenuation on terrestrial paths with irregular profiles is widely used the model of number successive absorbing knife-edge obstacles[1-6]. In the earlier paper concerning this problem it were suggested heuristic methods. Only in [3] successive using of Fresnel-Kirchoff theory for double diffraction was considered. More recently computation of multiple diffraction integral was
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S. Jonathan Chapman, J. R. Ockendon, V. H. Saward · The Journal of the Acoustical Society of America · 2000
Explicit formulas are derived for waves modeled by the scalar two-dimensional Helmholtz equation for the field that is diffracted when surface creeping rays encounter an infinitely sharp edge. Both Neumann and Dirichlet boundary conditions are analyzed, and the diffracted field is found to be an order to magnitude smaller in the latter case.
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Angler, Gábor · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011
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P. C. Clemmow · IRE Transactions on Antennas and Propagation · 1956
A comparatively simple method for obtaining an asymptotic approximation to the electromagnetic field diffracted by a large aperture in a perfectly conducting, infinitely thin, plane screen is suggested. The method is based on two assumptions: first, that in some regions the scattered field is nearly the same as the field that would be generated by certain currents located on the edge of the aperture; secondly, that at any point on the edge of the aperture these currents are nearly the same as the corresponding currents for a half-plane lying in the plane of the diffracting screen, the straight edge of which is locally coincident with the edge of the aperture. In the crudest approximation the calculation is made on the basis that the half-planes are excited by the incident field alone; higher order approximations arise from a consideration of the interaction between the different parts of the edge of the aperture. Applications of the method to the cases of a plane wave normally incident on (1) a slit of infinite length with parallel straight edges, and (2) a circular aperture are considered. In the former case several terms of the asymptotic development of the transmission cross section in inverse powers of the slit width are given; in the latter case the aperture and axial fields based on the zero-order approximation which neglects interaction are compared with experimental data published by various authors and with some rigorous calculations of Andrejewski.
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Rajaram Nityananda · Resonance · 2015
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Chapman, SJ, Ockendon, JR, Saward, VH · Oxford University Research Archive (ORA) (University of Oxford) · 2000
Explicit formulas are derived for waves modeled by the scalar two-dimensional Helmholtz equation for the field that is diffracted when surface creeping rays encounter an infinitely sharp edge. Both Neumann and Dirichlet boundary conditions are analyzed, and the diffracted field is found to be an order to magnitude smaller in the latter case.
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P. L. Christiansen · Proceedings of the IEEE · 1974
An analysis of the diffraction processes at a wedge in the geometrical theory of diffraction is presented. In the case where one wave mode can propagate outside a nonideally conducting wedge we show that the diffracted field can be viewed as consisting of a "nonreflected contribution" and a "reflected contribution." A generalization method from the one-mode case to the case where two modes of propagation exist outside the wedge is proposed. By means of this procedure we may construct the diffraction coefficients obtained by Labianca and Felsen for a conducting half-plane in a compressible plasma. The application of two-dimensional results to three-dimensional problems is summarized.
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Chapman Lawry, S. J. Chapman, J. M. H. Lawry et al. · 2007
The extension of the Geometrical Theory of Diffraction to complex rays is considered. The key difference with real rays arises in the determination of the regions of existence of the incident and reflected fields, which are governed by Stokes phenomenon. The procedure is demonstrated using the simple example of diffraction by a finite plate. 1 Introduction The application of traditional ray theory to diffraction problems has been well understood since the introduction of the Geometrical Theory of Diffraction (GTD) [?]. However, the need to obtain accurate computation, especially in deep shadows or in the dark extremities of beams or plane waves whose propagation angle is complex (henceforth referred to as complex plane waves), motivates the continuation of ray-theory asymptotic expansions to numbers of terms where algebraically small contributions in terms of the inverse wavenumber can be comparable to exponentially small ones. This can happen, for example, in the study of radar sca...
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A. S. Kryukovsky, D. S. Lukin · Journal of Communications Technology and Electronics · 2019
Abstract—The application of the wave theory of edge catastrophes to the asymptotic solution of diffraction problems on bodies with curvilinear edges is considered. As an example, the diffraction of a converging scalar wave on a curvilinear ideally conducting screen in a homogeneous medium is studied, leading to the formation of C4 and K4, 2 edge catastrophes.
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P. F. Daley, Edward S. Krebes · 2011
Diffractions make significant contributions to seismic amplitudes. While they are often not included in ray trace models due to their perceived computational diffi culty and expense, this paper describes a tractable method for computing diffractions which could benefit seismic modeling in exporation geophysics. We present formulae related to the diffraction of seismic waves by linear edges in elastodynamic media, based on an exten sion of the high frequency, zero order Asymptotic Ray Theory (ART) formulation. Theoretical development has been kept to a minimum. Rather, schematics indicating relevant details such as shadow boundaries and boundary rays have been included. The identification of the above is required as the argument of the diffraction coefficient is dependent on the angle between the shadow boundary ray and the diffracted ray or equivalently the difference between the diffracted and reflected arrival times. More will be said about this in the text. The reflected geometrical arrival does not exist in the shadow region and its travel time is required to determine the argument of the diffraction coefficient . Using analytic continuation, within the aforementioned limits of minimal theoretical discussion, this topic is also consid ered. Klem-Musatov (1980) derived a very comprehen sive set of formulae for the diffracted amplitude due to a linear edge in a three dimensional medium. This work was the basis of the PhD. Thesis of Chan (1986) where the theory, along with numerous numerical experiments involving the comparison of the modified ART solution with “exact” solution methods, was presented. A basic problem will first be considered to give a brief overview of the theory of edge diffractions. The geometry of this problem involves a wedge embedded in a halfspace and is such that both a source and receivers are located at the surface of the halfspace. Only reflected rays and primary diffractions are included in the solution. The motivation for this is to provide some initial insight for the extension of edge diffraction theory to more complicated and realistic geological structures. As an ART type solu tion is used, the geometrical and diffracted wavefields are computed separately and the total wavefield is the sum of the two. This concept can be extended to combining a number of diffracting edge models and additively obtain the total wavefield.
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Rius Casals, Juan Manuel, Carbo, Alex, Úbeda Farré, Eduard et al. · RECERCAT (Consorci de Serveis Universitaris de Catalunya)
This paper addresses two graphical processing approaches for computation of edge scattering with Physical Theory of Diffraction (PTD) high-frequency approximation. One is based on processing only a bitmap containing an image of the radar target, while the other uses a bitmap graphical processing algorithm to identify illuminated and shadowed facet mesh vertices, published in 2014, and then computes PTD diffraction coefficients for illuminated edges in the conventional way. The first approach is much faster for models containing a very large number of facets, but introduces pixel discretization noise, that can be alleviated by using larger bitmaps.
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E. Garmire, F. Karpushko, A. Kost et al. · Optical Society of America Annual Meeting · 1990
As much as 25% self-diffraction has been observed at the surface of n-GaAs:Te when two pumps (and a weak probe) intersect with an internal angle of 0.15 rad in the Raman–Nath regime. The photoinduced gratings decayed in less than 100 ps. The diffraction efficiency was nearly independent of sample thickness (40 μ m and 350 μ m), and careful investigation has shown that the diffraction arose primarily at the surface and was resonant just below the band edge. It is proposed that band-bending at the surface states causes increased absorption and results in a sheet of optically induced charge. The faster diffusion of electrons relative to holes allows a transient charge separation to a distance of one diffusion length (1 μ m). As a result, a space-charge field is formed (Dember field) that can cause an index change through the Franz–Keldysh effect. The resulting transient grating can cause the large observed diffraction. This new BEST effect has potential for optical-switching applications.
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F. Alonaizi, Roman Pevzner · Proceedings · 2015
Summary In this work a robust imaging algorithm based on detecting edge diffraction has been developed. The algorithm is based on measuring the coherency of the data using the semblance function computed along the traveltime curve of the diffracted wave. Based on the fact that waveforms on two sides of edge diffraction have opposite polarity, the proposed method exploit the phase-reversal phenomenon of edge diffractions in the computation process and use it as a criterion to separate edge diffractions from specular reflections. Utilizing the phase-reversal property of edge diffraction allows the detection of small features in the subsurface, and image hidden diffracted waves that could be masked by strong reflections. Two examples are provided to illustrate the validity of the method, the first example is a physical model of an edge diffractor, and the second example is real GPR data acquired over a lake.
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Jørgen Bach Andersen · IEEE Transactions on Antennas and Propagation · 1997
The uniform theory of diffraction (UTD) is applied to multiple absorbing screens, which are in the transition zones near shadow boundaries. The theory includes the application of slope diffraction, which is a first-order effect in transition zone diffraction. By choosing length parameters independently for amplitude and slope diffraction, it is ensured that the solution has continuity of amplitude and slope at each point. The solution is compared with known solutions with good results except when two screens are very near each other. The study is of particular interest to radio propagation over terrain in mobile radio systems.
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S.W. Rienstra · Journal of Fluid Mechanics · 1981
The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow. In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound. In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.
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John M. Arnold · Journal of the Optical Society of America A · 1992
Spectral methods for the construction of uniform asymptotic representations of the field diffracted by an aperture in a plane screen are reviewed. These are separated into contrasting approaches, roughly described as physical and geometrical. It is concluded that the geometrical methods provide a direct route to the construction of uniform representations that are formally identical to the equivalent-edge-current concept. Some interpretive and analytical difficulties that complicate the physical methods of obtaining uniform representations are analyzed. Spectral synthesis proceeds directly from the ray geometry and diffraction coefficients, without any intervening current representation, and the representation is uniform at shadow boundaries and caustics of the diffracted field. The physical theory of diffraction postulates currents on the diffracting screen that give rise to the diffracted field. The difficulties encountered in evaluating the current integrals are thoroughly examined, and it is concluded that the additional data provided by the physical theory of diffraction (diffraction coefficients off the Keller diffraction cone) are not actually required for obtaining uniform asymptotics at the leading order. A new diffraction representation that generalizes to arbitrary plane-convex apertures a formula given by Knott and Senior [ Proc. IEEE62, 1468 ( 1974)] for circular apertures is deduced.
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OhioLink ETD Center (Ohio Library and Information Network) · 2008
A knife edge is slowly moved into the laser beam as the laser light is viewed on a distant screen, as seen in Figure 1. As the knife edge is inserted into the beam, the diffraction pattern of the knife edge is observed on the screen.
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